The computation of bounds for the norm of the error in the conjugate gradient algorithm
The computation of bounds for the norm of the error in the conjugate gradient algorithm is considered. Section 2 recalls how to compute approximations of the A-norm and shows these approximations are lower and upper bounds. Section 3 shows how to compute approximations of the \(l_2\)-norm. Section 4 introduces an adaptive algorithm that computes estimates of the smallest eigenvalue that is needed to obtain upper bounds of the norm. Some numerical experiments showing the effectiveness of this approach are given in the last section.
scientific article; zbMATH DE number 1146039